Efficient analytical scatter modeling in fully 3-D iterative single photon emission computed tomography reconstruction

Quantitative single photon emission computed tomography (SPECT) images are degraded by several physical factors, among which Compton scatter is the most difficult to compensate. An analytical scatter modeling (ASM) method is proposed to model scatter in SPECT. The reconstruction architecture includes following steps: 1) a look-up table describing patient independent factors was precalculated, and a numerical integration method based on number theory resulted in 1 to 2 order of magnitude speed up in precalculation. 2) The transition matrix was generated based on the patient-specific attenuation map. 3) OSEM reconstruction was performed with an unmatched projector/backprojector. ASM was validated by Monte-Carlo simulation, considering the case of the point source in a homogeneous and a non-homogeneous medium. Experiment was performed using a HAMAMATSU BHP6601 SPECT and a SPECT performance phantom. Projection data was reconstructed by OSEM method with/without ASM, filtered back projection(FBP) and FBP with dual energy window (DEW) scatter correction. Results show that OSEM/ASM is more accurate and gain higher contrast than others. For a 64 ×64 × 64 image array. The computation time of the transition matrix is 80 min, and the reconstruction takes 4 min per iteration on a 1.54 GHz processor PC. This work proposed a computationally efficient method to model scatter in SPECT reconstruction within clinically acceptable time.